IKMC 2009 - Grades 11-12 - Paper 02 - Self-study Question 9

Extend the sides of triangle $ABC$ in both directions to $P,Q,R,S,T,U$, as shown, so that $PA=AB=BS$, $TC=CA=AQ$, and $UC=CB=BR$. If the area of $ABC$ is 1, what is the area of hexagon $PQRSTU$?